Problem: Factor completely. $16n^6+40n^3+25=$
$\begin{aligned} &\phantom{=}16 n ^6 + 40 n ^3 + 25 \\\\ &= ({4 n ^3})^2 + 2({4 n ^3})({5 })+({5 })^2 \end{aligned}$ Using the square of a sum pattern: $\begin{aligned} &\phantom{=}({4 n ^3})^2 + 2({4 n ^3})({5 })+({5 })^2 \\\\ &=({4 n ^3} + {5 })^2 \end{aligned}$ In conclusion, $16 n ^6 + 40 n ^3 + 25 =(4 n ^3 + 5 )^2$ Remember that you can always check your factorization by expanding it.